/* SPDX-License-Identifier: GPL-2.0 */
|
.file "reg_round.S"
|
/*---------------------------------------------------------------------------+
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| reg_round.S |
|
| |
|
| Rounding/truncation/etc for FPU basic arithmetic functions. |
|
| |
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| Copyright (C) 1993,1995,1997 |
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| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
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| Australia. E-mail billm@suburbia.net |
|
| |
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| This code has four possible entry points. |
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| The following must be entered by a jmp instruction: |
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| fpu_reg_round, fpu_reg_round_sqrt, and fpu_Arith_exit. |
|
| |
|
| The FPU_round entry point is intended to be used by C code. |
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| From C, call as: |
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| int FPU_round(FPU_REG *arg, unsigned int extent, unsigned int control_w) |
|
| |
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| Return value is the tag of the answer, or-ed with FPU_Exception if |
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| one was raised, or -1 on internal error. |
|
| |
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| For correct "up" and "down" rounding, the argument must have the correct |
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| sign. |
|
| |
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+---------------------------------------------------------------------------*/
|
|
/*---------------------------------------------------------------------------+
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| Four entry points. |
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| |
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| Needed by both the fpu_reg_round and fpu_reg_round_sqrt entry points: |
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| %eax:%ebx 64 bit significand |
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| %edx 32 bit extension of the significand |
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| %edi pointer to an FPU_REG for the result to be stored |
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| stack calling function must have set up a C stack frame and |
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| pushed %esi, %edi, and %ebx |
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| |
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| Needed just for the fpu_reg_round_sqrt entry point: |
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| %cx A control word in the same format as the FPU control word. |
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| Otherwise, PARAM4 must give such a value. |
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| |
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| |
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| The significand and its extension are assumed to be exact in the |
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| following sense: |
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| If the significand by itself is the exact result then the significand |
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| extension (%edx) must contain 0, otherwise the significand extension |
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| must be non-zero. |
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| If the significand extension is non-zero then the significand is |
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| smaller than the magnitude of the correct exact result by an amount |
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| greater than zero and less than one ls bit of the significand. |
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| The significand extension is only required to have three possible |
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| non-zero values: |
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| less than 0x80000000 <=> the significand is less than 1/2 an ls |
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| bit smaller than the magnitude of the |
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| true exact result. |
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| exactly 0x80000000 <=> the significand is exactly 1/2 an ls bit |
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| smaller than the magnitude of the true |
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| exact result. |
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| greater than 0x80000000 <=> the significand is more than 1/2 an ls |
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| bit smaller than the magnitude of the |
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| true exact result. |
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| |
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+---------------------------------------------------------------------------*/
|
|
/*---------------------------------------------------------------------------+
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| The code in this module has become quite complex, but it should handle |
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| all of the FPU flags which are set at this stage of the basic arithmetic |
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| computations. |
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| There are a few rare cases where the results are not set identically to |
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| a real FPU. These require a bit more thought because at this stage the |
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| results of the code here appear to be more consistent... |
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| This may be changed in a future version. |
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+---------------------------------------------------------------------------*/
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|
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#include "fpu_emu.h"
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#include "exception.h"
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#include "control_w.h"
|
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/* Flags for FPU_bits_lost */
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#define LOST_DOWN $1
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#define LOST_UP $2
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/* Flags for FPU_denormal */
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#define DENORMAL $1
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#define UNMASKED_UNDERFLOW $2
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|
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#ifndef NON_REENTRANT_FPU
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/* Make the code re-entrant by putting
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local storage on the stack: */
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#define FPU_bits_lost (%esp)
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#define FPU_denormal 1(%esp)
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#else
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/* Not re-entrant, so we can gain speed by putting
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local storage in a static area: */
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.data
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.align 4,0
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FPU_bits_lost:
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.byte 0
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FPU_denormal:
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.byte 0
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#endif /* NON_REENTRANT_FPU */
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|
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.text
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.globl fpu_reg_round
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.globl fpu_Arith_exit
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/* Entry point when called from C */
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ENTRY(FPU_round)
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pushl %ebp
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movl %esp,%ebp
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pushl %esi
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pushl %edi
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pushl %ebx
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movl PARAM1,%edi
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movl SIGH(%edi),%eax
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movl SIGL(%edi),%ebx
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movl PARAM2,%edx
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fpu_reg_round: /* Normal entry point */
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movl PARAM4,%ecx
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#ifndef NON_REENTRANT_FPU
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pushl %ebx /* adjust the stack pointer */
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#endif /* NON_REENTRANT_FPU */
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|
#ifdef PARANOID
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/* Cannot use this here yet */
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/* orl %eax,%eax */
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/* jns L_entry_bugged */
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#endif /* PARANOID */
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cmpw EXP_UNDER,EXP(%edi)
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jle L_Make_denorm /* The number is a de-normal */
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movb $0,FPU_denormal /* 0 -> not a de-normal */
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|
Denorm_done:
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movb $0,FPU_bits_lost /* No bits yet lost in rounding */
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movl %ecx,%esi
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andl CW_PC,%ecx
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cmpl PR_64_BITS,%ecx
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je LRound_To_64
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cmpl PR_53_BITS,%ecx
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je LRound_To_53
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cmpl PR_24_BITS,%ecx
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je LRound_To_24
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|
#ifdef PECULIAR_486
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/* With the precision control bits set to 01 "(reserved)", a real 80486
|
behaves as if the precision control bits were set to 11 "64 bits" */
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cmpl PR_RESERVED_BITS,%ecx
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je LRound_To_64
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#ifdef PARANOID
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jmp L_bugged_denorm_486
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#endif /* PARANOID */
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#else
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#ifdef PARANOID
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jmp L_bugged_denorm /* There is no bug, just a bad control word */
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#endif /* PARANOID */
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#endif /* PECULIAR_486 */
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|
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/* Round etc to 24 bit precision */
|
LRound_To_24:
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movl %esi,%ecx
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andl CW_RC,%ecx
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cmpl RC_RND,%ecx
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je LRound_nearest_24
|
|
cmpl RC_CHOP,%ecx
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je LCheck_truncate_24
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cmpl RC_UP,%ecx /* Towards +infinity */
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je LUp_24
|
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cmpl RC_DOWN,%ecx /* Towards -infinity */
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je LDown_24
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#ifdef PARANOID
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jmp L_bugged_round24
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#endif /* PARANOID */
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|
LUp_24:
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cmpb SIGN_POS,PARAM5
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jne LCheck_truncate_24 /* If negative then up==truncate */
|
|
jmp LCheck_24_round_up
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LDown_24:
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cmpb SIGN_POS,PARAM5
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je LCheck_truncate_24 /* If positive then down==truncate */
|
|
LCheck_24_round_up:
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movl %eax,%ecx
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andl $0x000000ff,%ecx
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orl %ebx,%ecx
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orl %edx,%ecx
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jnz LDo_24_round_up
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jmp L_Re_normalise
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LRound_nearest_24:
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/* Do rounding of the 24th bit if needed (nearest or even) */
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movl %eax,%ecx
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andl $0x000000ff,%ecx
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cmpl $0x00000080,%ecx
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jc LCheck_truncate_24 /* less than half, no increment needed */
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|
jne LGreater_Half_24 /* greater than half, increment needed */
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/* Possibly half, we need to check the ls bits */
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orl %ebx,%ebx
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jnz LGreater_Half_24 /* greater than half, increment needed */
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orl %edx,%edx
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jnz LGreater_Half_24 /* greater than half, increment needed */
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/* Exactly half, increment only if 24th bit is 1 (round to even) */
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testl $0x00000100,%eax
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jz LDo_truncate_24
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LGreater_Half_24: /* Rounding: increment at the 24th bit */
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LDo_24_round_up:
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andl $0xffffff00,%eax /* Truncate to 24 bits */
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xorl %ebx,%ebx
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movb LOST_UP,FPU_bits_lost
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addl $0x00000100,%eax
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jmp LCheck_Round_Overflow
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LCheck_truncate_24:
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movl %eax,%ecx
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andl $0x000000ff,%ecx
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orl %ebx,%ecx
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orl %edx,%ecx
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jz L_Re_normalise /* No truncation needed */
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|
LDo_truncate_24:
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andl $0xffffff00,%eax /* Truncate to 24 bits */
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xorl %ebx,%ebx
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movb LOST_DOWN,FPU_bits_lost
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jmp L_Re_normalise
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|
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/* Round etc to 53 bit precision */
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LRound_To_53:
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movl %esi,%ecx
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andl CW_RC,%ecx
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cmpl RC_RND,%ecx
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je LRound_nearest_53
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cmpl RC_CHOP,%ecx
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je LCheck_truncate_53
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cmpl RC_UP,%ecx /* Towards +infinity */
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je LUp_53
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cmpl RC_DOWN,%ecx /* Towards -infinity */
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je LDown_53
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#ifdef PARANOID
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jmp L_bugged_round53
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#endif /* PARANOID */
|
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LUp_53:
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cmpb SIGN_POS,PARAM5
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jne LCheck_truncate_53 /* If negative then up==truncate */
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|
jmp LCheck_53_round_up
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LDown_53:
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cmpb SIGN_POS,PARAM5
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je LCheck_truncate_53 /* If positive then down==truncate */
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|
LCheck_53_round_up:
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movl %ebx,%ecx
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andl $0x000007ff,%ecx
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orl %edx,%ecx
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jnz LDo_53_round_up
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jmp L_Re_normalise
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LRound_nearest_53:
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/* Do rounding of the 53rd bit if needed (nearest or even) */
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movl %ebx,%ecx
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andl $0x000007ff,%ecx
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cmpl $0x00000400,%ecx
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jc LCheck_truncate_53 /* less than half, no increment needed */
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|
jnz LGreater_Half_53 /* greater than half, increment needed */
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/* Possibly half, we need to check the ls bits */
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orl %edx,%edx
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jnz LGreater_Half_53 /* greater than half, increment needed */
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/* Exactly half, increment only if 53rd bit is 1 (round to even) */
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testl $0x00000800,%ebx
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jz LTruncate_53
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LGreater_Half_53: /* Rounding: increment at the 53rd bit */
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LDo_53_round_up:
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movb LOST_UP,FPU_bits_lost
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andl $0xfffff800,%ebx /* Truncate to 53 bits */
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addl $0x00000800,%ebx
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adcl $0,%eax
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jmp LCheck_Round_Overflow
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LCheck_truncate_53:
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movl %ebx,%ecx
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andl $0x000007ff,%ecx
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orl %edx,%ecx
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jz L_Re_normalise
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LTruncate_53:
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movb LOST_DOWN,FPU_bits_lost
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andl $0xfffff800,%ebx /* Truncate to 53 bits */
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jmp L_Re_normalise
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|
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/* Round etc to 64 bit precision */
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LRound_To_64:
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movl %esi,%ecx
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andl CW_RC,%ecx
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cmpl RC_RND,%ecx
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je LRound_nearest_64
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cmpl RC_CHOP,%ecx
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je LCheck_truncate_64
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cmpl RC_UP,%ecx /* Towards +infinity */
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je LUp_64
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cmpl RC_DOWN,%ecx /* Towards -infinity */
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je LDown_64
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#ifdef PARANOID
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jmp L_bugged_round64
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#endif /* PARANOID */
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LUp_64:
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cmpb SIGN_POS,PARAM5
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jne LCheck_truncate_64 /* If negative then up==truncate */
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|
orl %edx,%edx
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jnz LDo_64_round_up
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jmp L_Re_normalise
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LDown_64:
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cmpb SIGN_POS,PARAM5
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je LCheck_truncate_64 /* If positive then down==truncate */
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|
orl %edx,%edx
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jnz LDo_64_round_up
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jmp L_Re_normalise
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LRound_nearest_64:
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cmpl $0x80000000,%edx
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jc LCheck_truncate_64
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jne LDo_64_round_up
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/* Now test for round-to-even */
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testb $1,%bl
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jz LCheck_truncate_64
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LDo_64_round_up:
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movb LOST_UP,FPU_bits_lost
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addl $1,%ebx
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adcl $0,%eax
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LCheck_Round_Overflow:
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jnc L_Re_normalise
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/* Overflow, adjust the result (significand to 1.0) */
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rcrl $1,%eax
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rcrl $1,%ebx
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incw EXP(%edi)
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jmp L_Re_normalise
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LCheck_truncate_64:
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orl %edx,%edx
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jz L_Re_normalise
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LTruncate_64:
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movb LOST_DOWN,FPU_bits_lost
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L_Re_normalise:
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testb $0xff,FPU_denormal
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jnz Normalise_result
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L_Normalised:
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movl TAG_Valid,%edx
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L_deNormalised:
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cmpb LOST_UP,FPU_bits_lost
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je L_precision_lost_up
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cmpb LOST_DOWN,FPU_bits_lost
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je L_precision_lost_down
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L_no_precision_loss:
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/* store the result */
|
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L_Store_significand:
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movl %eax,SIGH(%edi)
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movl %ebx,SIGL(%edi)
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|
cmpw EXP_OVER,EXP(%edi)
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jge L_overflow
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|
movl %edx,%eax
|
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/* Convert the exponent to 80x87 form. */
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addw EXTENDED_Ebias,EXP(%edi)
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andw $0x7fff,EXP(%edi)
|
|
fpu_reg_round_signed_special_exit:
|
|
cmpb SIGN_POS,PARAM5
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je fpu_reg_round_special_exit
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orw $0x8000,EXP(%edi) /* Negative sign for the result. */
|
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fpu_reg_round_special_exit:
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#ifndef NON_REENTRANT_FPU
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popl %ebx /* adjust the stack pointer */
|
#endif /* NON_REENTRANT_FPU */
|
|
fpu_Arith_exit:
|
popl %ebx
|
popl %edi
|
popl %esi
|
leave
|
ret
|
|
|
/*
|
* Set the FPU status flags to represent precision loss due to
|
* round-up.
|
*/
|
L_precision_lost_up:
|
push %edx
|
push %eax
|
call set_precision_flag_up
|
popl %eax
|
popl %edx
|
jmp L_no_precision_loss
|
|
/*
|
* Set the FPU status flags to represent precision loss due to
|
* truncation.
|
*/
|
L_precision_lost_down:
|
push %edx
|
push %eax
|
call set_precision_flag_down
|
popl %eax
|
popl %edx
|
jmp L_no_precision_loss
|
|
|
/*
|
* The number is a denormal (which might get rounded up to a normal)
|
* Shift the number right the required number of bits, which will
|
* have to be undone later...
|
*/
|
L_Make_denorm:
|
/* The action to be taken depends upon whether the underflow
|
exception is masked */
|
testb CW_Underflow,%cl /* Underflow mask. */
|
jz Unmasked_underflow /* Do not make a denormal. */
|
|
movb DENORMAL,FPU_denormal
|
|
pushl %ecx /* Save */
|
movw EXP_UNDER+1,%cx
|
subw EXP(%edi),%cx
|
|
cmpw $64,%cx /* shrd only works for 0..31 bits */
|
jnc Denorm_shift_more_than_63
|
|
cmpw $32,%cx /* shrd only works for 0..31 bits */
|
jnc Denorm_shift_more_than_32
|
|
/*
|
* We got here without jumps by assuming that the most common requirement
|
* is for a small de-normalising shift.
|
* Shift by [1..31] bits
|
*/
|
addw %cx,EXP(%edi)
|
orl %edx,%edx /* extension */
|
setne %ch /* Save whether %edx is non-zero */
|
xorl %edx,%edx
|
shrd %cl,%ebx,%edx
|
shrd %cl,%eax,%ebx
|
shr %cl,%eax
|
orb %ch,%dl
|
popl %ecx
|
jmp Denorm_done
|
|
/* Shift by [32..63] bits */
|
Denorm_shift_more_than_32:
|
addw %cx,EXP(%edi)
|
subb $32,%cl
|
orl %edx,%edx
|
setne %ch
|
orb %ch,%bl
|
xorl %edx,%edx
|
shrd %cl,%ebx,%edx
|
shrd %cl,%eax,%ebx
|
shr %cl,%eax
|
orl %edx,%edx /* test these 32 bits */
|
setne %cl
|
orb %ch,%bl
|
orb %cl,%bl
|
movl %ebx,%edx
|
movl %eax,%ebx
|
xorl %eax,%eax
|
popl %ecx
|
jmp Denorm_done
|
|
/* Shift by [64..) bits */
|
Denorm_shift_more_than_63:
|
cmpw $64,%cx
|
jne Denorm_shift_more_than_64
|
|
/* Exactly 64 bit shift */
|
addw %cx,EXP(%edi)
|
xorl %ecx,%ecx
|
orl %edx,%edx
|
setne %cl
|
orl %ebx,%ebx
|
setne %ch
|
orb %ch,%cl
|
orb %cl,%al
|
movl %eax,%edx
|
xorl %eax,%eax
|
xorl %ebx,%ebx
|
popl %ecx
|
jmp Denorm_done
|
|
Denorm_shift_more_than_64:
|
movw EXP_UNDER+1,EXP(%edi)
|
/* This is easy, %eax must be non-zero, so.. */
|
movl $1,%edx
|
xorl %eax,%eax
|
xorl %ebx,%ebx
|
popl %ecx
|
jmp Denorm_done
|
|
|
Unmasked_underflow:
|
movb UNMASKED_UNDERFLOW,FPU_denormal
|
jmp Denorm_done
|
|
|
/* Undo the de-normalisation. */
|
Normalise_result:
|
cmpb UNMASKED_UNDERFLOW,FPU_denormal
|
je Signal_underflow
|
|
/* The number must be a denormal if we got here. */
|
#ifdef PARANOID
|
/* But check it... just in case. */
|
cmpw EXP_UNDER+1,EXP(%edi)
|
jne L_norm_bugged
|
#endif /* PARANOID */
|
|
#ifdef PECULIAR_486
|
/*
|
* This implements a special feature of 80486 behaviour.
|
* Underflow will be signalled even if the number is
|
* not a denormal after rounding.
|
* This difference occurs only for masked underflow, and not
|
* in the unmasked case.
|
* Actual 80486 behaviour differs from this in some circumstances.
|
*/
|
orl %eax,%eax /* ms bits */
|
js LPseudoDenormal /* Will be masked underflow */
|
#else
|
orl %eax,%eax /* ms bits */
|
js L_Normalised /* No longer a denormal */
|
#endif /* PECULIAR_486 */
|
|
jnz LDenormal_adj_exponent
|
|
orl %ebx,%ebx
|
jz L_underflow_to_zero /* The contents are zero */
|
|
LDenormal_adj_exponent:
|
decw EXP(%edi)
|
|
LPseudoDenormal:
|
testb $0xff,FPU_bits_lost /* bits lost == underflow */
|
movl TAG_Special,%edx
|
jz L_deNormalised
|
|
/* There must be a masked underflow */
|
push %eax
|
pushl EX_Underflow
|
call EXCEPTION
|
popl %eax
|
popl %eax
|
movl TAG_Special,%edx
|
jmp L_deNormalised
|
|
|
/*
|
* The operations resulted in a number too small to represent.
|
* Masked response.
|
*/
|
L_underflow_to_zero:
|
push %eax
|
call set_precision_flag_down
|
popl %eax
|
|
push %eax
|
pushl EX_Underflow
|
call EXCEPTION
|
popl %eax
|
popl %eax
|
|
/* Reduce the exponent to EXP_UNDER */
|
movw EXP_UNDER,EXP(%edi)
|
movl TAG_Zero,%edx
|
jmp L_Store_significand
|
|
|
/* The operations resulted in a number too large to represent. */
|
L_overflow:
|
addw EXTENDED_Ebias,EXP(%edi) /* Set for unmasked response. */
|
push %edi
|
call arith_overflow
|
pop %edi
|
jmp fpu_reg_round_signed_special_exit
|
|
|
Signal_underflow:
|
/* The number may have been changed to a non-denormal */
|
/* by the rounding operations. */
|
cmpw EXP_UNDER,EXP(%edi)
|
jle Do_unmasked_underflow
|
|
jmp L_Normalised
|
|
Do_unmasked_underflow:
|
/* Increase the exponent by the magic number */
|
addw $(3*(1<<13)),EXP(%edi)
|
push %eax
|
pushl EX_Underflow
|
call EXCEPTION
|
popl %eax
|
popl %eax
|
jmp L_Normalised
|
|
|
#ifdef PARANOID
|
#ifdef PECULIAR_486
|
L_bugged_denorm_486:
|
pushl EX_INTERNAL|0x236
|
call EXCEPTION
|
popl %ebx
|
jmp L_exception_exit
|
#else
|
L_bugged_denorm:
|
pushl EX_INTERNAL|0x230
|
call EXCEPTION
|
popl %ebx
|
jmp L_exception_exit
|
#endif /* PECULIAR_486 */
|
|
L_bugged_round24:
|
pushl EX_INTERNAL|0x231
|
call EXCEPTION
|
popl %ebx
|
jmp L_exception_exit
|
|
L_bugged_round53:
|
pushl EX_INTERNAL|0x232
|
call EXCEPTION
|
popl %ebx
|
jmp L_exception_exit
|
|
L_bugged_round64:
|
pushl EX_INTERNAL|0x233
|
call EXCEPTION
|
popl %ebx
|
jmp L_exception_exit
|
|
L_norm_bugged:
|
pushl EX_INTERNAL|0x234
|
call EXCEPTION
|
popl %ebx
|
jmp L_exception_exit
|
|
L_entry_bugged:
|
pushl EX_INTERNAL|0x235
|
call EXCEPTION
|
popl %ebx
|
L_exception_exit:
|
mov $-1,%eax
|
jmp fpu_reg_round_special_exit
|
#endif /* PARANOID */
|
|
ENDPROC(FPU_round)
|
